A posteriori error analysis for nonlinear systems of hyperbolic conservation laws

Datum
Veranstaltungsort
Magdeburg

Der Vortrag findet in Gebäude 02, Raum 210 statt.

Vortragender

Herrn Prof. Dr. Jan Giesselmann [FMA]

Veranstalter: FMA

Nonlinear systems of hyperbolic conservation laws are an important mathematical tool in many areas of physics and engineering, most notably in compressible fluid mechanics.

This talk deals with a posteriori error estimates for Discontinuous Galerkin schemes for systems of hyperbolic conservation laws. The estimates that we present are based on the relative entropy stability framework which we combine with reconstructions of numerical solutions. In this way, we obtain computable upper bounds for the error which are optimal in a sense which will be made precise in the talk.

If time permits, we discuss how the methods that were discussed before can be extended to problems with random initial data. We will put particular emphasis on decomposing the overall error estimator into parts which quantify stochastic discretization errors and space-time discretization errors, respectively. We present numerical evidence that the error estimators scale as predicted by our analysis.


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